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The air pollution in a city is caused mainly by industrial (I) and automobile (A) exhausts....

The air pollution in a city is caused mainly by industrial (I) and automobile (A) exhausts. In the next 5 years, the chances of successfully controlling these two sources of pollution are, respectively, 75% and 60%. Assume that if only one of the two sources is successfully controlled, the probability of bringing the pollution below acceptable level would be 80%. If both sources are controlled successfully, the pollution is assumed to reach below the acceptable level (E). If both sources are not controlled successfully, it is assumed the pollution will not reach the acceptable level (E). Ignore all other factors.
(a) What is the probability of successfully controlling air pollution in the next 5 years, P(E)? (i.e., the pollution is brought down to acceptable level).
(b) If, in the next 5 years, the pollution level is not sufficiently controlled, what is the probability that is entirely caused by the failure to control automobile exhaust?
(c) If air pollution (E) is not controlled, what is the probability that control of automobile exhaust (A) was not successful?

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